# Norm forms for arbitrary number fields as products of linear polynomials

@article{Browning2013NormFF, title={Norm forms for arbitrary number fields as products of linear polynomials}, author={T. Browning and Lilian Matthiesen}, journal={arXiv: Number Theory}, year={2013} }

Let K/Q be a field extension of finite degree and let P(t) be a polynomial over Q that splits into linear factors over Q. We show that any smooth model of the affine variety defined by the equation N_{K/Q} (k) = P(t) satisfies the Hasse principle and weak approximation whenever the Brauer-Manin obstruction is empty. Our proof is based on a combination of methods from additive combinatorics due to Green-Tao and Green-Tao-Ziegler, together with an application of the descent theory of Colliot-Th… Expand

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